The veteran midfielder has been one of the key players for Rangers this season and was again in fine form in their 4-0 win over Ross County on Sunday.
Rangers boss Steven Gerrard picked out Davis for praise after the game and Rough believes it was important as the midfielder’s work can often go unnoticed in games.
He pointed towards the midfielder’s consistency and how he keeps things simple during a game, which can often mean that he is hardly noticed for his performances.
Rough stressed while the goalscorers and the creative players earn the plaudits, Davis’ work at the base of Rangers’ midfield remains underappreciated by many.
The former goalkeeper said on PLZ Soccer when asked about a superb pass from the Rangers midfielder against Ross County: “He is the kind of player and it is the kind of pass that we all want to see.
“He must be a great guy inside the dressing room and even on the park, he just does the simple things.
“He just does everything correctly.
“In fact, when you are watching a game, you hardly notice him at all.
“When he is on the ball he does the simple things, but he has got that pass in him as well.
“Steven Gerrard was right in coming out and singling him out at the weekend because he does go a wee bit unnoticed when you have got the likes of [James] Tavernier, [Alfredo] Morelos and all of them.
“I think the manager really appreciates, him being a midfielder, how much he puts into the game.”
Davis will be looking to cap off his return to Rangers by lifting the Scottish Premiership title at the end of the season.
